In a resonace air column experiment, first and second resonances are obtained at lengths of air columns l1 and l2, the third resonance will be obtained at a length of

Question

In a resonace air column experiment, first and second resonances are obtained at lengths of air columns l1 and l2, the third resonance will be obtained at a length of (A) 2l2-l1 (B) l2-2l+1 (C) l2-l1 (D) 3l2-l1

Tardigrade Admin · Accepted Answer

l1 +e = (λ/4) ⇒ (1) l2 + e = (3 λ/4) ⇒ (2) from (1) , (2) sub e, λ in l3 + e = (5 λ/4)

Q. In a resonace air column experiment, first and second resonances are obtained at lengths of air columns $l_{1}$ and $l_{2}$ , the third resonance will be obtained at a length of

$2 l_{2} - l_{1}$

$l_{2} - 2 l + 1$

$l_{2} - l_{1}$

$3 l_{2} - l_{1}$

$l_{1} + e = \frac{λ}{4}$ $\Rightarrow$ (1)
$l_{2} + e = \frac{3 λ}{4}$ $\Rightarrow$ (2)
from (1) , (2) sub e, $λ$ in
$l_{3} + e = \frac{5 λ}{4}$

Q. In a resonace air column experiment, first and second resonances are obtained at lengths of air columns l1​ and l2​, the third resonance will be obtained at a length of

2l2​−l1​

l2​−2l+1

l2​−l1​

3l2​−l1​